Preston has been on my mind since the 2021 release of Peter Jackson’s docuseries “The Beatles: Get Back,” which served, among other things, as a reminder just how crucial the Texas-born keyboard prodigy was to the “Let It Be” sessions. (Given his effortless playing style and the good-natured way he diffused tension on the studio, John Lennon basically asked him to join the band.) But I’ve been listening to Preston, and specifically his Beatles covers, after catching a preview screening of Paris Barclay’s documentary about his charmed but troubled life, “Billy Preston: That’s the Way God Planned It,” which will be playing in New York later this month.